\[ \DeclareMathOperator{\argmin}{argmin} \DeclareMathOperator{\Var}{Var} \DeclareMathOperator{\Cor}{Cor} \]

Bibliography

Allaire, J. J., Charles Teague, Carlos Scheidegger, Yihui Xie, and Christophe Dervieux. 2024. Quarto.” https://doi.org/10.5281/zenodo.5960048.
Anderson, Marti J. 2001. “Permutation Tests for Univariate or Multivariate Analysis of Variance and Regression.” Canadian Journal of Fisheries and Aquatic Sciences 58 (3): 626–39. https://doi.org/10.1139/f01-004.
Bates, Douglas, Martin Mächler, Ben Bolker, and Steve Walker. 2015. “Fitting Linear Mixed-Effects Models Using lme4.” Journal of Statistical Software 67 (1): 1–48. https://doi.org/10.18637/jss.v067.i01.
Benjamini, Yoav, Ruth Heller, and Daniel Yekutieli. 2009. “Selective Inference in Complex Research.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1906): 4255–71. https://doi.org/10.1098/rsta.2009.0127.
Box, G. E. P. 1953. “Non-Normality and Tests on Variances.” Biometrika 40 (3/4): 318–35.
Box, G. E. P., and D. R. Cox. 1964. “An Analysis of Transformations.” Journal of the Royal Statistical Society. Series B (Methodological) 26 (2): 211–52.
Box, George E. P., William Gordon Hunter, and J. Stuart Hunter. 1978. Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building. Wiley Series in Probability and Mathematical Statistics. New York, NY: Wiley.
Bretz, Frank, Torsten Hothorn, and Peter H. Westfall. 2011. Multiple Comparisons Using R. Boca Raton, FL: CRC Press.
Brooks, Mollie E., Kasper Kristensen, Koen J. van Benthem, Arni Magnusson, Casper W. Berg, Anders Nielsen, Hans J. Skaug, Martin Maechler, and Benjamin M. Bolker. 2017. glmmTMB Balances Speed and Flexibility Among Packages for Zero-Inflated Generalized Linear Mixed Modeling.” The R Journal 9 (2): 378–400. https://journal.r-project.org/archive/2017/RJ-2017-066/index.html.
Burdick, Richard K., and Franklin A. Graybill. 1992. Confidence Intervals on Variance Components. Statistics, Textbooks and Monographs 127. New York: M. Dekker.
Dalgaard, Peter. 2008. Introductory Statistics with R. 2nd ed. Statistics and Computing. New York, NY: Springer.
de Mendiburu, Felipe. 2020. Agricolae: Statistical Procedures for Agricultural Research. https://CRAN.R-project.org/package=agricolae.
Dobson, A. J. 1983. Introduction to Statistical Modelling. New York, NY: Springer.
Dunnett, Charles W. 1955. “A Multiple Comparison Procedure for Comparing Several Treatments with a Control.” Journal of the American Statistical Association 50 (272): 1096–1121. https://doi.org/10.1080/01621459.1955.10501294.
Edgington, E., and P. Onghena. 2007. Randomization Tests. Statistics: A Series of Textbooks and Monographs. Boca Raton, FL: CRC Press.
Faraway, Julian James. 2005. Linear Models with R. Texts in Statistical Science. Boca Raton, FL: Chapman & Hall/CRC.
Federer, Walter Theodore, and Freedom King. 2007. Variations on Split Plot and Split Block Experiment Designs. Wiley Series in Probability and Statistics. Hoboken, NJ: Wiley-Interscience.
Fitzmaurice, Garrett M., Nan M. Laird, and James H. Ware. 2011. Applied Longitudinal Analysis. Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons, Inc. https://doi.org/10.1002/9781119513469.
Fox, John, and Sanford Weisberg. 2019. An R Companion to Applied Regression. Third. Thousand Oaks, CA: Sage. https://socialsciences.mcmaster.ca/jfox/Books/Companion/.
Goos, Peter, Ivan Langhans, and Martina Vandebroek. 2006. “Practical Inference from Industrial Split-Plot Designs.” Journal of Quality Technology 38 (2): 162–79.
Green, Peter, and Catriona J. MacLeod. 2016. “Simr: An R Package for Power Analysis of Generalised Linear Mixed Models by Simulation.” Methods in Ecology and Evolution 7 (4): 493–98. https://doi.org/10.1111/2041-210X.12504.
Hayter, Anthony J. 1984. “A Proof of the Conjecture That the Tukey-Kramer Multiple Comparisons Procedure Is Conservative.” The Annals of Statistics 12 (1): 61–75. https://www.jstor.org/stable/2241034.
Henderson, Charles R. 1963. “Selection Index and Expected Genetic Advance.” In Statistical Genetics and Plant Breeding, edited by W. D. Hanson and H. F. Robinson, 141–63. 982. National Academy of Sciences-National Research Council, Washington, D.C.
Holm, Sture. 1979. “A Simple Sequentially Rejective Multiple Test Procedure.” Scandinavian Journal of Statistics 6 (2): 65–70. http://www.jstor.org/stable/4615733.
Hothorn, Torsten, Frank Bretz, and Peter Westfall. 2008. “Simultaneous Inference in General Parametric Models.” Biometrical Journal 50 (3): 346–63.
Hsu, J. 1996. Multiple Comparisons: Theory and Methods. Guilford School Practitioner. Boca Raton, FL: Chapman; Hall/CRC Press. https://books.google.ch/books?id=8AK8PUbw3lsC.
Huitema, Bradley E. 2011. The Analysis of Covariance and Alternatives: Statistical Methods for Experiments, Quasi-Experiments, and Single-Case Studies. Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons, Inc. https://doi.org/10.1002/9781118067475.
Jiang, Jiming, and Thuan Nguyen. 2021. Linear and Generalized Linear Mixed Models and Their Applications. Springer Series in Statistics. New York, NY: Springer. https://doi.org/10.1007/978-1-0716-1282-8.
Jones, Bradley, and Christopher Nachtsheim. 2009. “Split-Plot Designs: What, Why, and How.” Journal of Quality Technology 41 (4): 340–61. https://doi.org/10.1080/00224065.2009.11917790.
Jones, Byron, and Michael Kenward. 2014. Design and Analysis of Cross-over Trials. Third. Chapman & Hall / CRC Monographs on Statistics and Applied Probability 138. Boca Raton, FL: CRC Press/Taylor & Francis.
Keane, Bil. 1998. “The Family Circus.” Cowles Syndicate.
Kramer, Clyde Young. 1956. “Extension of Multiple Range Tests to Group Means with Unequal Numbers of Replications.” Biometrics 12 (3): 307. https://doi.org/10.2307/3001469.
Kuehl, Robert. 2000. Design of Experiments: Statistical Principles of Research Design and Analysis. Statistics Series. Duxbury/Thomson Learning.
Kuznetsova, Alexandra, Per B. Brockhoff, and Rune H. B. Christensen. 2017. lmerTest Package: Tests in Linear Mixed Effects Models.” Journal of Statistical Software 82 (13): 1–26. https://doi.org/10.18637/jss.v082.i13.
Lakens, Daniel, and Aaron Caldwell. 2021. “Simulation-Based Power Analysis for Factorial Analysis of Variance Designs.” Advances in Methods and Practices in Psychological Science 4 (1): 1–14. https://doi.org/10.1177/2515245920951503.
Lawson, J. 2014. Design and Analysis of Experiments with R. Chapman & Hall/CRC Texts in Statistical Science. Boca Raton, FL: CRC Press/Taylor & Francis.
Lawson, John, and Gerhard Krennrich. 2021. Daewr: Design and Analysis of Experiments with r. https://CRAN.R-project.org/package=daewr.
Lenth, Russell V. 2020. Emmeans: Estimated Marginal Means, Aka Least-Squares Means. https://CRAN.R-project.org/package=emmeans.
Loy, Adam, and Heike Hofmann. 2014. HLMdiag: A Suite of Diagnostics for Hierarchical Linear Models in R.” Journal of Statistical Software 56 (5): 1–28. https://www.jstatsoft.org/article/view/v056i05.
———. 2015. “Are You Normal? The Problem of Confounded Residual Structures in Hierarchical Linear Models.” Journal of Computational and Graphical Statistics 24 (4): 1191–1209. https://www.jstor.org/stable/24737225.
Loy, Adam, Heike Hofmann, and Dianne Cook. 2017. “Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners.” Journal of Computational and Graphical Statistics 26 (3): 478–92. https://doi.org/10.1080/10618600.2017.1330207.
Mandal, B N. 2019. ibd: Incomplete Block Designs. https://CRAN.R-project.org/package=ibd.
Montgomery, Douglas. 2019. Design and Analysis of Experiments. Hoboken, NJ: Wiley.
Oehlert, Gary. 2000. A First Course in Design and Analysis of Experiments. New York, NY: W.H. Freeman. http://users.stat.umn.edu/~gary/book/fcdae.pdf.
Pearl, Judea, and Dana Mackenzie. 2018. The Book of Why: The New Science of Cause and Effect. 1st ed. New York, NY: Basic Books, Inc.
Pinheiro, J., and D. Bates. 2009. Mixed-Effects Models in S and S-PLUS. Statistics and Computing. New York, NY: Springer.
Pinheiro, J., D. Bates, S. DebRoy, D. Sarkar, and R Core Team. 2021. Nlme: Linear and Nonlinear Mixed Effects Models. https://CRAN.R-project.org/package=nlme.
R Core Team. 2021. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.
Rice, J. A. 2007. Mathematical Statistics and Data Analysis. Advanced Series. Boston, MA: Cengage Learning.
Robinson, G. K. 1991. “That BLUP Is a Good Thing: The Estimation of Random Effects.” Statistical Science 6 (1): 15–32. https://doi.org/10.1214/ss/1177011926.
Sailer, Martin Oliver. 2013. Crossdes: Construction of Crossover Designs. https://CRAN.R-project.org/package=crossdes.
Santos Nobre, Juvêncio, and Julio da Motta Singer. 2007. “Residual Analysis for Linear Mixed Models.” Biometrical Journal 49 (6): 863–75. https://doi.org/10.1002/bimj.200610341.
Scheffé, H. 1959. The Analysis of Variance. New York, NY: John Wiley & Sons.
Scheipl, Fabian, Sonja Greven, and Helmut Kuechenhoff. 2008. “Size and Power of Tests for a Zero Random Effect Variance or Polynomial Regression in Additive and Linear Mixed Models.” Computational Statistics & Data Analysis 52 (7): 3283–99.
Signorell, Andri et al. 2021. DescTools: Tools for Descriptive Statistics. https://cran.r-project.org/package=DescTools.
Speed, M, R Hocking, and P Hackney. 1978. “Methods of Analysis of Linear Models with Unbalanced Data.” Journal of the American Statistical Association 73 (361): 105–12. https://doi.org/10.1080/01621459.1978.10480012.
Stolley, Paul D. 1991. “When Genius Errs: R. A. Fisher and the Lung Cancer Controversy.” American Journal of Epidemiology 133 (5): 416–25. https://doi.org/10.1093/oxfordjournals.aje.a115904.
Tukey, John W. 1949a. “Comparing Individual Means in the Analysis of Variance.” Biometrics 5 (2): 99–114.
———. 1949b. “One Degree of Freedom for Non-Additivity.” Biometrics 5 (3): 232–42. http://www.jstor.org/stable/3001938.
Venables, W. N., and B. D. Ripley. 2002. Modern Applied Statistics with S. Fourth. New York, NY: Springer. https://www.stats.ox.ac.uk/pub/MASS4/.
Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. New York, NY: Springer. https://ggplot2.tidyverse.org.
Xie, Yihui. 2015. Dynamic Documents with R and Knitr. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC Press. http://yihui.name/knitr/.
———. 2021. Bookdown: Authoring Books and Technical Documents with r Markdown. https://CRAN.R-project.org/package=bookdown.
Yates, F. 1935. “Complex Experiments.” Supplement to the Journal of the Royal Statistical Society 2 (2): 181–247. http://www.jstor.org/stable/2983638.